New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite element analysis of 3D frictional contact problem

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 1-4, 2011, Pages 77-88

  Zhang, H W ^a   Li, J Y ^a,b   Pan, S H ^c  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b TIANJIN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

3D frictional contact problems; Complementarity; Parametric variational principle; Second order cone; Semi smooth Newton method

Indexed keywords

COMPLEMENTARITY; FRICTIONAL CONTACT PROBLEMS; SECOND ORDER CONE; SEMISMOOTH NEWTON METHOD; VARIATIONAL PRINCIPLES;

FRICTION; FUNCTIONS; NEWTON-RAPHSON METHOD; THREE DIMENSIONAL; VARIATIONAL TECHNIQUES;

FINITE ELEMENT METHOD;

EID: 78649631363     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.07.014     Document Type: Article

References (32)

1. Wriggers P. Computational Contact Mechanics 2002, Wiley, New York.
2. Alart P., Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Computer Methods Appl. Mech. Engrg. 1991, 92:353-375.
3. Simo J.C., Laursen T.A. An augmented Lagrangian treatment of contact problems involving friction. Comput. Struct. 1992, 42:97-116.
4. De Saxcé G., Feng Z.-Q. The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms. Math. Comput. Model. 1998, 28:225-245.
5. Kikuchi N., Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Elements 1988, SIAM, Philadelphia.
6. Zhong W.X., Sun S.M. A finite element method for elasto-plastic structure and contact problem by parametric quadratic programming. Int. J. Numer. Methods Engrg. 1988, 26:2723-2738.
7. Klarbring A. A mathematical programming approach to three-dimensional contact problems with friction. Comput. Methods Appl. Mech. Engrg. 1986, 58:175-200.
8. Kwak B.M. Complementarity problem formulation of three dimensional frictional contact. ASME J. Appl. Mech. 1991, 58:134-140.
9. Zhang H.W., Zhong W.X., Gu Y.X. A combined parametric quadratic programming and iteration method for 3-D elastic-plastic frictional contact problem analysis. Comput. Methods Appl. Mech. Engrg. 1998, 155:307-324.
10. Chen W.J., Chen G.Q., Feng E.M. variational principle with nonlinear complementarity for three-dimensional contact problems and its numerical method. Sci. China (Ser. A) 1996, 39:528-539.
11. Glocker C. Formulation of spatial contact situations in rigid multibody systems. Comput. Methods Appl. Mech. Engrg. 1999, 177:199-214.
12. Park J.K., Kwak B.M. Three-dimensional frictional contact analysis using the homotopy method. ASME J. Appl. Mech. 1994, 61:703-709.
13. Strömberg N. A Newton method for three-dimensional fretting problems. Int. J. Solids Struct. 1999, 36:2075-2090.
14. Johansson L., Klarbring A. Study of frictional impact using a nonsmooth equations solver. ASME J. Appl. Mech. 2000, 67:267-273.
15. Leung A.Y.T., Chen G.Q., Chen W.J. Smoothing Newton method for solving two- and three-dimensional frictional contact problems. Int. J. Numer. Methods Engrg. 1998, 41:1001-1027.
16. Christensen P.W., Pang J.-S. Frictional contact algorithms based on semismooth Newton methods. Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods 1999, 81-116. Kluwer Academic Publishers, Boston, MA. M. Fukushima, L. Qi (Eds.).
17. Koziara Tomasz, Bićanić Nenad Semismooth Newton method for frictional contact between pseudo-rigid bodies. Comput. Methods Appl. Mech. Engrg. 2008, 197:2763-2777.
18. Kanno Y., Martins J.A.C., Pinto da Costa A. Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem. Int. J. Numer. Methods Engrg. 2006, 65:62-83.
19. Belytschko T., Mish K. Computability in non-linear solid mechanics. Int. J. Numer. Methods Engrg. 2001, 52:3-21.
20. Zhang H.W., Zhong W.X., Wu C.H., Liao A.H. Some advances and applications in quadratic programming method for numerical modeling of elastoplastic contact problems. Int. J. Mech. Sci. 2006, 48:176-189.
21. Fukushima M., Luo Z.Q., Tseng P. Smoothing functions for second-order cone complementarity problems. SIAM J. Optim. 2002, 12:436-460.
22. Hayashi S., Yamashita N., Fukushima M. A combined smoothing and regularization method for monotone second-order cone complementarity problems. SIAM J. Optim. 2005, 15:593-615.
23. Chen J.S., Tseng P. An unconstrained smooth minimization reformulation of the second-order cone complementarity problem. Math. Program. 2005, 104:293-327.
24. Pan S.H., Chen J.S. A semismooth Newton method for SOCCPs based on a one-parametric class of complementarity functions. Comput. Optim. Appl. 2010, 45:59-88.
25. Faraut J., Korányi A. Analysis on Symmetric Cones. Oxford Mathematical Monographs 1994, Oxford University Press, New York.
26. Sun D., Qi L.Q. On NCP-functions. Comput. Optim. Appl. 1999, 13:201-220.
27. Laursen T.A. Computational Contact and Impact Mechanics 2002, Springer-Verlag, Berlin, Heidelberg.
28. Curnier A. Unilateral contact-mechanical modeling. New Developments in Contact Problems 1999, Springer-Wien, New York. P. Wriggers, P.D. Panagiotopoulos (Eds.).
29. Ben-Tal A., Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications 2001, SIAM, Philadelphia.
30. Zhang H.W., He S.Y., Li X.S. Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation. Comput. Methods Appl. Mech. Engrg. 2005, 194(50-52):5139-5158.
31. Chen J.S., Pan S.H. A one-parametric class of merit functions for the second-order cone complementarity problem. Comput. Optim. Appl. 2010, 45:581-606.
32. Nocedal J., Wright S.J. Numerical Optimization 1999, Springer.